4.OA.3: Multi-Step Word Problems

Visual Models for Multi-Step Problems

1. Tape Diagrams (Bar Models)

These are rectangular bars that represent quantities in the problem. They help visualize the relationships between quantities and can be especially helpful for problems involving addition, subtraction, and multiplicative comparison.

2. Number Lines

Useful for showing addition, subtraction, and even multiplication (as repeated jumps). They help your child see the operations in sequence.

3. Arrays

Rows and columns of objects that help visualize multiplication and division. For example, to represent 6 boxes with 12 items in each, draw 6 rows with 12 dots in each row.

Example Problem with Visual Model:

"A store received 6 boxes of notebooks with 12 notebooks in each box. They sold 45 notebooks. How many notebooks are left?"

Step 1: Draw 6 boxes with 12 dots in each to represent 6 × 12 = 72 notebooks total

Step 2: Cross out 45 dots to represent the notebooks sold

Step 3: Count the remaining dots: 72 - 45 = 27 notebooks left

Real-World Applications

1. Real-Life Math

Create word problems based on everyday situations:

• Grocery shopping (calculating total cost, change, comparing prices)
• Cooking (adjusting recipes, calculating serving sizes)
• Planning a party (calculating costs for food, decorations, etc.)

2. Math Journal

Keep a journal where your child writes out word problems, draws visual models, and shows their solution process. This helps them organize their thinking and track their progress.

3. Using Variables

Practice writing equations with variables for simple situations around the house:

• "If you have s stickers and give 5 to your sister, you have s - 5 left."
• "If you save $3 each week, after w weeks you'll have 3w dollars."

When Your Child Struggles

The CUBES Strategy:

• C - Circle the numbers
• U - Underline the question
• B - Box the key words that indicate operations
• E - Evaluate the steps needed
• S - Solve and check your answer

Alternative: The READ Strategy:

• R - Read the problem carefully
• E - Extract the important information
• A - Analyze what operations to use
• D - Draw or write an equation and solve

Breaking Down the Problem:

Help your child identify the steps needed to solve the problem:

1. What information is given?
2. What are we trying to find?
3. What operations do we need to use first? Second?
4. How can we check our answer?

5-Minute Activities

Key Words and Operations

Addition Key Words: Sum, total, in all, altogether, increased by, more than

Subtraction Key Words: Difference, how much more, left, remain, decreased by, less than, fewer than

Multiplication Key Words: Product, times, multiplied by, of, groups of, at this rate

Division Key Words: Quotient, divided by, per, out of, ratio, average, equal groups

Quick Activity: Problem Creation

Have your child create their own multi-step word problems. This helps them understand the structure of these problems from the inside out.

Quick Activity: Equation Match

Write several word problems and several equations with variables. Have your child match each problem with the correct equation.

Mid-Year Expectations

By the middle of the school year, your child should be able to:

• Read a multi-step word problem and identify the key information
• Determine which operations to use in simple two-step problems
• Solve basic two-step word problems involving addition and subtraction
• Represent simple problems with equations using a letter for the unknown

End-of-Year Expectations

By the end of the school year, your child should be able to:

• Solve multi-step word problems using all four operations
• Write equations with a letter for the unknown quantity
• Use appropriate visual models to represent problems
• Check the reasonableness of their answers
• Explain their solution process

Signs of Mastery

Your child has mastered this standard when they can:

• Independently solve complex multi-step word problems
• Accurately represent problems with equations using variables
• Determine which operations to use and in what order
• Verify their solutions and explain why they make sense
• Create their own multi-step word problems
• Apply problem-solving strategies to real-world situations

Questions to Check Understanding:

• A theater has 25 rows with 16 seats in each row. If 327 tickets were sold, how many empty seats remain?
• A school ordered 18 boxes of pencils with 24 pencils in each box. If each of the 36 students receives 10 pencils, how many pencils will be left?
• Emma saved $15 each week for 6 weeks. She spent $27 on a new game and $18 on a book. How much money does she have left?

Below Grade Level

For students who need additional support with basic multi-step word problems and using variables.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level multi-step word problems using all four operations.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging multi-step word problems and more complex variables.

📥 Download Challenge Worksheet